## Annals of Statistics

### A Complete Class Theorem for Estimating a Noncentrality Parameter

Mo Suk Chow

#### Abstract

In statistical decision theory, an important question is to characterize the admissible rules. In this paper, we establish complete class theorems for estimating the noncentrality parameter of noncentral chi-square and noncentral $F$ distributions under squared error loss. Under a minor assumption, any admissible estimator must be a generalized Bayes rule. Using this result, we prove that the positive part of the UMVUE is inadmissible.

#### Article information

Source
Ann. Statist., Volume 15, Number 2 (1987), 800-804.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176350375

Digital Object Identifier
doi:10.1214/aos/1176350375

Mathematical Reviews number (MathSciNet)
MR888440

Zentralblatt MATH identifier
0627.62008

JSTOR